5:19 AM
-3

I think these tags (uvw and sos) are useful for the forum. User, which looks for to learn these methods, can click these tags and see many examples, how he can prove inequalities by these methods. For example. Let we need to prove that $$a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(... The main problem I see there is that (theoretically) we could have question where all of the tags , , , , fit. We would use all 5 places for tag even without adding the main tag. @MichaelRozenberg since you have most experience with inequality question, you are in a good position to judge whether creating too many too specific tags could lead to this. (Or whether this already is a problem.) You might notice that this is one of the things raised in the question on meta: > One more thing to keep in mind is that question can have at most five tags. So if we create too many very specific tags, it might happen that on some question we will not have enough space to add all tags which might be suitable there. How many methods do you plan to add as tags? You mention ev-method here: 0 I want to create a new tag EV-Method, but I want to know before, what Community thinks about it. This method is very useful for the proof of hard symmetric inequalities with n variables. I think if our user will want to learn this method he'll can click this tag and see many examples, how to u... Do you plan to add abc-method (a.k.a. abstract concreteness method), smv-method (strong mixing variables)? My other question about these methods is to which extent are these names standard. For example, I do not see ev-method in Cvetkovski's book. (I have already mentioned this in a comment under your post about ev-method.) 5 hours later… 10:33 AM Karamata's inequality has tag-excerpt and tag-wiki. And also tangent-line-method has tag-excerpt and tag-wiki. 0 I have been reading a book on some classic inequalties and i have stumbled upon this: Let f:[0, +\infty]\rightarrow \mathbf R be a convex function and x_1,x_2,...,x_n a sequence of positive numbers. It can be proved that :$$\sum_{i=1}^nf(x_i) \le (n- 1)f(0) + f(\sum_{i=1}^nx_i)$$This is appa... 3 It is given that, x+y+z=3\quad 0\le x, y, z \le 2 and we are to maximise x^3+y^3+z^3. My attempt : if we define f(x, y, z) =x^3+y^3 +z^3 with x+y+z=3 it can be shown that, f(x+z, y, 0)-f(x,y,z)=3xz(x+z)\ge 0 and thus f(x, y, z) \le f(x+z, y, 0). This implies that f attains it's ... 0 Given x,y,z are positive number satisfy x^2+y^2+z^2=1. Prove that$$\frac{x}{y^2+z^2}+\frac{y}{z^2+x^2}+\frac{z}{x^2+y^2}\ge \frac{3\sqrt{3}}{2} i need a way use reduction of many fractions to a common denominator

0

$a, b,c$ are positive real numbers such that $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$ Any ideas ?